Definition:Extended Real Number Line/Definition 1

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The extended real number line $\overline \R$ is defined as:

$\overline \R := \R \cup \set {+\infty, -\infty}$

that is, the set of real numbers together with two auxiliary symbols:

$+\infty$, positive infinity
$-\infty$, negative infinity

such that:

$\forall x \in \R: x < +\infty$
$\forall x \in \R: -\infty < x$

Also see

  • Results about extended real numbers can be found here.